9,211 research outputs found
Kinetic energy operator approach to the quantum three-body problem with Coulomb interactions
We present a non-variational, kinetic energy operator approach to the
solution of quantum three-body problem with Coulomb interactions, based on the
utilization of symmetries intrinsic to the kinetic energy operator, i.e., the
three-body Laplacian operator with the respective masses. Through a four-step
reduction process, the nine dimensional problem is reduced to a one dimensional
coupled system of ordinary differential equations, amenable to accurate
numerical solution as an infinite-dimensional algebraic eigenvalue problem. A
key observation in this reduction process is that in the functional subspace of
the kinetic energy operator where all the rotational degrees of freedom have
been projected out, there is an intrinsic symmetry which can be made explicit
through the introduction of Jacobi-spherical coordinates. A numerical scheme is
presented whereby the Coulomb matrix elements are calculated to a high degree
of accuracy with minimal effort, and the truncation of the linear equations is
carried out through a systematic procedureComment: 56 pages, 11 figure
The genesis of the quantum theory of the chemical bond
An historical overview is given of the relevant steps that allowed the
genesis of the quantum theory of the chemical bond, starting from the
appearance of the new quantum mechanics and following later developments till
approximately 1931. General ideas and some important details are discussed
concerning molecular spectroscopy, as well as quantum computations for simple
molecular systems performed within perturbative and variational approaches, for
which the Born-Oppenheimer method provided a quantitative theory accounting for
rotational, vibrational and electronic states. The novel concepts introduced by
the Heitler-London theory, complemented by those underlying the method of the
molecular orbitals, are critically analyzed along with some of their relevant
applications. Further improvements in the understanding of the nature of the
chemical bond are also considered, including the ideas of one-electron and
three-electron bonds introduced by Pauling, as well as the generalizations of
the Heitler-London theory firstly performed by Majorana, which allowed the
presence of ionic structures into homopolar compounds and provided the
theoretical proof of the stability of the helium molecular ion. The study of
intermolecular interactions, as developed by London, is finally examined.Comment: amsart, 34 pages, 2 figure
Spin and rotational symmetries in unrestricted Hartree Fock states of quantum dots
Ground state energies are obtained using the unrestricted Hartree Fock method
for up to four interacting electrons parabolically confined in a quantum dot
subject to a magnetic field. Restoring spin and rotational symmetries we
recover Hund first rule. With increasing magnetic field, crossovers between
ground states with different quantum numbers are found for fixed electron
number that are not reproduced by the unrestricted Hartree Fock approximation.
These are consistent with the ones obtained with more refined techniques. We
confirm the presence of a spin blockade due to a spin mismatch in the ground
states of three and four electrons.Comment: 16 Pages, 2 figures, accepted for publication on New Journal of
Physic
Floating Wigner molecules and possible phase transitions in quantum dots
A floating Wigner crystal differs from the standard one by a spatial
averaging over positions of the Wigner-crystal lattice. It has the same
internal structure as the fixed crystal, but contrary to it, takes into account
rotational and/or translational symmetry of the underlying jellium background.
We study properties of a floating Wigner molecule in few-electron
spin-polarized quantum dots, and show that the floating solid has the lower
energy than the standard Wigner crystal with fixed lattice points. We also
argue that internal rotational symmetry of individual dots can be broken in
arrays of quantum dots, due to degenerate ground states and inter-dot Coulomb
coupling.Comment: 6 pages incl 3 figure
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